Problem: The perimeter of a rectangle is $34$ units. Its width is $6.5$ units. Write an equation to determine the length $(l)$ of the rectangle. Find the length of the rectangle.
Explanation: Let $l$ be the length of the rectangle. The perimeter is equal to $2l+2w$. Let's substitute in the width of $6.5$ : $ \begin{aligned}&2l+2w\\ =&2l+2(6.5)\\ =&2l+13\end{aligned}$ The perimeter of the rectangle is $2l+{13}$. Since the perimeter equals $34$ units, let's set this equal to $34$ : $ 2l+13=34$ Now, let's solve the equation to find the length of the rectangle $(l)$. $\begin{aligned} 2l+13&=34\\ \\ 2l+13{-13}&=34{-13}&&{\text{subtract }13} \text{ from each side}\\ \\ 2l&=21\\ \\ \dfrac{2l}{{2}}&=\dfrac{21}{{2}}&&\text{divide each side by ${2}$}\\ \\ l&=10.5\end{aligned}$ The equation is $2l+13=34$. The length of the rectangle is $10.5$ units.